The article makes that same comparison. The big difference with previous HLA's is they now have high performance aircraft on board. Pretty significant - no need to risk an expensive super carrier in many cases but still remain nearly as militarily effective.
WW2 CVLs were an attempt to get more flight decks into the ocean faster, anticipating war in the Pacific and expecting the Essex class carriers to take a bit longer than they did (IIRC, USS Independence came into commission around the same time USS Essex did). Being adaptations and just a bit more than half the size of the Essexes the Independence class were less capable, but they certainly achieved the goal of having lots of flight decks on the ocean. Task Force 38/58 usually had on the order of 14 or 15 carriers.
This new America class is purpose-built and appear to have been designed to support F-35s (as well as Ospreys and helicopters). With the Wasp class, which does have a well deck, also being able to support F-35s, this does spread their capability across a lot more flight decks, with (apparently) lower cost than a full-sized Nimitz or Ford CVN. It also untethers the CVNs from support of Marine landing operations, a function WW2 escort carriers performed - flexibility.